They are called Goodwill Guides. Your description is spot on. They only want to have travel etc paid for. But you will not only find students but also retirees and housewives.
I know one page with a huge list. Here is another one of such sites that covers several areas of Japan. If you are in Tokyo, you might want to go directly to this page.
Credit:stackoverflow.com‘
4 Mar, 2024
5 Mar, 2024
4 Mar, 2024